We have modelled the hard X-ray background expected for a high-altitude
balloon flight of the Energetic X-ray Imaging Telescope Experiment (EXITE2),
an imaging phoswich detector/telescope for the 20--600 keV energy range.
Photon
and neutron-induced contributions to the background are considered.
We describe the code and the results
of a series of simulations with different shielding configurations. The
simulated hard X-ray background for the actual flight configuration agrees
reasonably well (within a factor of $\sim$ 2) with the results measured on the
first flight of EXITE2 from Palestine, Texas. The measured
background flux at 100 keV is $\sim$ 4 $\times$ 10$^{-4}$ counts cm$^{-2}$ s$^{-1}$ keV$^{-1}$.\\